How would you play this river? I'll explain the reasoning behind my play below.

Opponent is relatively unknown.

PokerStars No-Limit Hold'em, $2 BB (6 handed) FTR converter on zerodivide.cx

CO ($280)
Button ($450.45)
SB ($39.45)
BB ($178.60)
UTG ($57.20)
Hero ($262.65)

Preflop: Hero is MP with A, A.
UTG calls $2, Hero raises to $8, 1 fold, Button calls $8, 2 folds, UTG folds.

Flop: ($21) 4, 6, 7 (2 players)
Hero bets $12, Button calls $12.

Turn: ($45) A (2 players)
Hero bets $18, Button calls $18.

River: ($81) A (2 players)
Hero bets $224.65 (All-In), Button calls $224.65.

Final Pot: $530.30

Results in white below:
Hero has Ah As (four of a kind, aces).
Button has Td Kd (flush, ace high).
Outcome: Hero wins $530.30.

Preflop and flop plays are standard. He called me quickly on the flop, which usually suggests a draw, so I put him on either two diamonds, or some kind of suited connector containing a 5. He may've flopped a set, but I suspect he would've at least thought about raising given the highly coordinated nature of the flop. The turn card was an ace of diamonds, which I obviously had mixed feelings about. I make a bet, and he again calls. Would he continue chasing a straight now with 3 diamonds on board and only one card to come? Many players will often give up on straight draws at this point, so I considered his call highly suspicious, and started to think he may've been slow-playing a flush. A set seems very improbable at this point. On the river, I make quads, but this pairs the board, which, if he has a flush, would be a concern for him. I realize that he isn't committing anymore money with a busted straight draw, so my only concern now is winning the maximum from a flush. I could make a small bet designed to induce a raise, and then come over the top, but he would become concerned about the full house and slow down, or perhaps even fold. Instead, I don't give him the chance to gain anymore information about my hand and simply put him to a decision for all my chips.